How to animate an object to dissapear (clipped progressively) as it passes through a plane?
Note: This answer is only convenient if your object is made of a single (or just a few) materials, and if the plane it intersects is parallel to two cartesian axes:



All you need to do is to Mix your material (in this case, a simple principled shader) with a fully white Transparent BDSF.

The Mix Factor must be controlled by a Math > (Greater/Less) than node, that compares your object's Geometry > Separate XYZ > [selected coordinate] with a fixed value. 

In this example, Z is compared with 0:



Additional notes:


If you are using Cycles and you see some black spots, you may need to increase a bit the number of Transmission bounces under Render > Light Paths.
If you are using EEVEE, your material's setting should have Blend Mode and Shadow Mode set to Alpha Clip.